learnpn (Neural Network Toolbox)

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learnpn

Examples See Also

Normalized perceptron weight/bias learning function

Syntax

[dW,LS] = learnpn(W,P,Z,N,A,T,E,gW,gA,D,LP,LS)

info = learnpn(code)

Description

learnpn is a weight/bias learning function. It can result in faster learning than learnp when input vectors have widely varying magnitudes.

learnpn(W,P,Z,N,A,T,E,gW,gA,D,LP,LS) takes several inputs,

W - S x R weight matrix (or S x 1 bias vector).

P - R x Q input vectors (or ones(1,Q)).

Z - S x Q weighted input vectors.

N - S x Q net input vectors.

A - S x Q output vectors.

T - S x Q layer target vectors.

E - S x Q layer error vectors.

gW - S x R weight gradient with respect to performance.

gA - S x Q output gradient with respect to performance.

D - S x S neuron distances.

LP - Learning parameters, none, LP = [].

LS - Learning state, initially should be = [].

and returns,

dW - S x R weight (or bias) change matrix.

LS - New learning state.

learnpn(code) returns useful information for each code string:

'pnames' - Names of learning parameters.

'pdefaults' - Default learning parameters.

'needg' - Returns 1 if this function uses gW or gA.

Examples

Here we define a random input P and error E to a layer with a 2-element input and 3 neurons.

p = rand(2,1);
e = rand(3,1);

Since learnpn only needs these values to calculate a weight change (see algorithm below), we will use them to do so.

dW = learnpn([],p,[],[],[],[],e,[],[],[],[],[])

Network Use

You can create a standard network that uses learnpn with newp.

To prepare the weights and the bias of layer i of a custom network to learn with learnpn:

1.: Set net.trainFcn to 'trainwb'. (net.trainParam will automatically become trainwb's default parameters.)

2.: Set net.adaptFcn to 'adaptwb'. (net.adaptParam will automatically become trainwb's default parameters.)

3.: Set each net.inputWeights{i,j}.learnFcn to 'learnpn'. Set each net.layerWeights{i,j}.learnFcn to 'learnpn'. Set net.biases{i}.learnFcn to 'learnpn'. (Each weight and bias learning parameter property will automatically become the empty matrix since learnpn has no learning parameters.)

To train the network (or enable it to adapt):

1.: Set net.trainParam (net.adaptParam) properties to desired values.

2.: Call train (adapt).

See newp for adaption and training examples.

Algorithm

learnpn calculates the weight change dW for a given neuron from the neuron's input P and error E according to the normalized perceptron learning rule:

pn = p / sqrt(1 + p(1)^2 + p(2)^2) + ... + p(R)^2)
dw =  0,   if e =  0
=  pn', if e =  1
= -pn', if e = -1

The expression for dW can be summarized as:

dw = e*pn'

Limitations

Perceptrons do have one real limitation. The set of input vectors must be linearly separable if a solution is to be found. That is, if the input vectors with targets of 1 cannot be separated by a line or hyperplane from the input vectors associated with values of 0, the perceptron will never be able to classify them correctly.